作业帮1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/04 23:58:20
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)=1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)=
1又1/2+2又1/4+3又1/8+L L+(n+1/2^n)
=(1+2+3+...+n)+(1/2+1/4+1/8+...+1/2^n)
=n(n+1)/2+(1/2^n-1)
1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+n)
1+2+3+.+n=n(n+1)
1/(1+2+3+...+n)=1/n(n+1)=1/n-1/(n+1)
所以
原式=1+1/1-1/2+1/2-1/3+1/3-1/4+.+1/n-1/(n-1)
=1+1+1/n
=2+1/n